Oka coherence theorem

In mathematics, specifically algebraic geometry, the Oka coherence theorem, proved by Kiyoshi Oka in 1950,^[1] states that the sheaf ${\displaystyle {\mathcal {O}}_{\mathbb {C} ^{n}}}$ of holomorphic functions on ${\displaystyle \mathbb {C} ^{n}}$ (and subsequently the sheaf ${\displaystyle {\mathcal {O}}_{X}}$ of holomorphic functions on a complex manifold ${\displaystyle X}$) is coherent.^[2][3]